I don't understand why you should say 'man geht ins Kino' instead of 'man geht in dem Kino'.

When using articles in German one has to think about whether the sentence needs to be accusative or dative. In the example above the first version is in the accusative and the second is in the dative. It is important to understand that the sentence is to do with movement so therefore the accusative should be used rather than the dative which is used when one is stationary. Another important thing to note is that 'ins' is short for 'in das' but when these two words are next to each other they are compressed together to make 'ins'.Had the sentence been 'man ist I'm Kino' then im is correct because the person is stationary and so the dative is used. Again, 'Im' is the condensed version of 'in dem'.